Disc integration, also known in integral calculus as the disc method, is a means of calculating the volume of a solid of revolution of a solid-state material when integrating along the axis of revolution. This method models the resulting three-dimensional shape as a "stack" of an infinite number of disks of varying radius and infinitesimal thickness. It is also possible to use the same principles with "washers" instead of "disks" (the "washer method") to obtain "hollow" solids of revolutions.

To obtain a “hollow” solid of revolution (the “washer method”), the procedure would be to take the volume of the inner solid of revolution and subtract it from the volume of the outer solid of revolution. This can be calculated in a single integral similar to the following:

where is the function that is farthest from the axis of rotation and is the function that is closest to the axis of rotation. One should take caution not to evaluate the square of the difference of the two functions, but to evaluate the difference of the squares of the two functions.

This formula only works for revolutions about the x-axis.

To rotate about any horizontal axis, simply subtract from that axis each formula:

if is the value of a horizontal axis, then the volume equals

For example, to rotate the region between and

along the axis , one would integrate as follows:

The bounds of integration are the zeros of the first equation minus the second. Note that when you integrate along an axis other than the , the further axis may not be that obvious. In the previous example, even though is further up than , it is the inner axis since it is closer to

The same idea can be applied to both the y-axis and any other vertical axis. One simply must solve each equation for before one inserts them into the integration formula.